Modified Fast Inertial‐Type Krasnosel’skii‐Mann Iterative Scheme Involving Asymptotically Nonexpansive Mapping
[EN] t is our aim to propose a new iterative algorithm with an inertial term involving asymptotically nonexpansive mapping in theframework of Hilbert spaces. Let T: H ⟶ H be asymptotically nonexpansive mapping with F(T) ≠ � and let x n n≥0 be definedby x n+1 = �nz n + b n T n�nz n − �nz n + �n, ∀ n...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:dnet:buleria_____::24c2519291086d62b9675ddc616e547f |
| Acceso en línea: | https://hdl.handle.net/10612/28490 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemáticas Asymptotically nonexpansive mapping Fixed point problem Hilbert space Krasnosel’skii-mann algorithm Monotone mapping Step-size parameter Variational inequality problem 12 Matemáticas |
| Sumario: | [EN] t is our aim to propose a new iterative algorithm with an inertial term involving asymptotically nonexpansive mapping in theframework of Hilbert spaces. Let T: H ⟶ H be asymptotically nonexpansive mapping with F(T) ≠ � and let x n n≥0 be definedby x n+1 = �nz n + b n T n�nz n − �nz n + �n, ∀ n ≥ 1. T satisfies an additional mild condition, then the sequence x n n≥0 convergesstrongly to x ≔ P F(T)(0). Our main contribution lies in establishing a strong convergence theorem for this method, without rely-ing on the assumption that ∑∞n=1�k2n − 1�. Our strong convergence theorems extend the corresponding convergence theorems inliterature for nonexpansive maps to a more general class of asymptotically nonexpansive maps. Furthermore, our proposed algo-rithm is implemented by finding the fixed point of common solutions to a variational inequality problem and � −inverse-stronglymonotone mapping in Hilbert space. Numerical illustrations showed some improvements over existing results in literature. |
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